I've already ruled out internships at most tech companies b/c
1. I spent a gap year working at a wide range of companies (big company, startup, research lab)
2. I'm a reasonably good programmer with open-source projects and while I'm quite sure I have a lot lot more to learn, I don't think a tech internship is the highest-leverage use of my time
3. (most important reason) I'm not sure I want to be a SWE. I love software engineering / programming, but when I think of the way to make the most impact in the world it's probably creating a (actually meaningful) startup/organization. (I know, I know, every young person says this these days)
Given that this is the case, I'm trying to figure out what to do this summer besides a normal tech internship. I was contemplating how to figure out what to do and decided on a "meta-strategy" of consulting people with more experience on forums such as HN.
Here are the options I've come up with so far:
1. Try to understand virality -- I'm not particularly good at creating viral content or content that appeals to the masses (aside from the natural edge that comes from being young), which could certainly be useful when marketing a product. An option here is trying to intern at a company like Buzzfeed which is full of people who understand emotions / virality.
2. Try to understand soft skills / business -- There are roles out there like "business development intern". I don't know anything about "business development" but negotiating with other companies / writing white-papers / etc. could be a useful skill
3. Spend time learning on my own. To enact change these days, it's probably not sufficient to just know programming (unless you want to do a SASS). Spending time on my own learning physics/chemistry/biology could be useful. The issue here is I believe mentorship is useful and this option negates that completely.
4. Working on my own business (not a software project). I've done this in the past & learned a lot about how to be scrappy. Not a terrible idea, but I don't want to sink 3 months into something only to have to return to school. Also negates mentorship. Also I'd rather spend time learning right now so I can execute on something that's not a local maximum of what my brain can imagine right now.
Out of curiosity I looked you up, look man, given your resume you're essentially set for life. You literally can do everything you want. But you need to live a little bit imo. You're what, 20-21yo? Relax.
Spend time with some friends, if you have some, try dating? traveling?
You've essentially achieved more than +99.9% of people at your age.(and actually a lot more than most people at any age)
In a few years from now I don't think you'll regret not having taken one more course or made one more project, but you'll probably regret not having enjoyed your summers, or your evening/nights, or spending more time with people you care about in a friendly setting.
On another thread you ask why overwork kills people...do you really want to find out?
You seem to be trying to over-optimise your time and talk about wanting to change things, there is a good chance you'll get burnt out and there is more to life than writing code and solving problems. I have no idea about you other than the context of your post so I may be completely wrong though.
I know you mentioned working at a research lab but have you tried more academic research? You seem to value learning and mentorship a lot, so it could be a lot of fun to pick a professor and work with them for a summer. Given your background, you could probably convince any STEM professor to work with you, and I would heavily recommend exploring stuff outside your area of expertise.
Best of luck!